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An angle is its own complement. The measure of the angle is

(a) 30°
(b) 45°
(c) 90°
(d) 60°

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Solution

$\begin{array}{l} (b) 45 ° \end{array} Suppose the angle is x ° . Then, the complement is also x ° . Complement of x ° = 90 ° - x ° \Rightarrow x ° = 90 ° - x ° \Rightarrow x ° + x ° = 90 ° \Rightarrow 2 x ° = 90 ° \Rightarrow x = \frac{90}{2} \Rightarrow x = 45$

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The measure of an angle which is its own complement is
(a) $30^{\circ}$
(b) $60^{\circ}$
(c) $90^{\circ}$
(d) $45^{\circ}$

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An angle is 24° more than its complement. The measure of the angle is

(a) 47°
(b) 57°
(c) 53°
(d) 66°

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An angle is one-fifth of its supplement. The measure of the angle is

(a) 30°
(b) 15°
(c) 75°
(d) 150°

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An angle is 32° less than its supplement. The measure of the angle is

(a) 37°
(b) 74°
(c) 148°
(d) none of these

The sum of an angle and one third of its supplementary angle is $90^{\circ}$ . The measure of the angle is
(a) $135^{\circ}$
(b) $120^{\circ}$
(c) $60^{\circ}$
(d) $45^{\circ}$

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Mark (✓) against the correct answer An angle is its own complement. The measure of the angle is (a) 30° (b) 45° (c) 90° (d) 60°

(b)45°Suppose the angle is x°.Then, the complement is also x°.Complement of x°=90°-x°⇒x°=90°-x°⇒x°+x°=90°⇒2x°=90°⇒x=902⇒x=45

Mark (✓) against the correct answer
An angle is its own complement. The measure of the angle is

(a) 30°
(b) 45°
(c) 90°
(d) 60°

$\begin{array}{l} (b) 45 ° \end{array} Suppose the angle is x ° . Then, the complement is also x ° . Complement of x ° = 90 ° - x ° \Rightarrow x ° = 90 ° - x ° \Rightarrow x ° + x ° = 90 ° \Rightarrow 2 x ° = 90 ° \Rightarrow x = \frac{90}{2} \Rightarrow x = 45$